In recent years, the analysis of signal properties (especially biomedical signals) has become an important research direction. One interesting feature of signals is their potential to be chaotic. This article concerns the issues of classification of real signals or synthetic ones in the context of detecting chaotic properties. In previous works, datasets of synthetic signals were created based on well-known chaotic and non-chaotic dynamical systems. They were published and used to train classifiers. This paper extends the previous studies and proposes a method for obtaining/extracting signals to force classifiers to learn to detect chaos. The proposed method allows the generation of groups of signals with similar initial conditions. The property of chaotic dynamical systems was used here, which consists of the strong dependence of the signal courses on a small change in the initial conditions. This method is based on reconstructing multidimensional phase space and data clustering. An additional goal of the work is to create referential datasets with so-called refined signals using the described method and to make them publicly available. The usefulness of the new datasets was confirmed during a simple experiment with the usage of the LSTM neural network.